Case two for second-order would occur for a reaction involving two reactants: A + B P 241

Case two for second-order would occur for a reaction involving two reactants: A + B P 242

Case two for second-order would occur for a reaction involving two reactants: A + B P The integrated rate law becomes 243

Case two for second-order would occur for a reaction involving two reactants: A + B P The integrated rate law becomes For this more complicated case it is necessary to keep track of two different concentrations. 244

Half-Lives 245

Half-Lives Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration. 246

Half-Lives Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration. Zero-order reaction: put in the expression leads to the result: 247

First-order reaction: put in the expression 248

First-order reaction: put in the expression leads to the result: 249

Decomposition of N 2 O 5 (first-order kinetics). 250

Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. 251

Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. 252

Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. Example: 253

Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. Example: This is a beta-decay where denotes an electron. 131 is the mass number = number of protons + number of neutrons; 53 is the atomic number. 254

255 Radioisotope usage to image the thyroid gland. The thyroid gland absorbs ions, which undergo beta decay that exposes a photographic film.

256

257

Theory of Chemical Reaction Rates 258

Theory of Chemical Reaction Rates The effect of temperature 259

Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation 260

Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation Nearly all reactions proceed faster at higher temperatures. 261

Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation Nearly all reactions proceed faster at higher temperatures. As a rough rule – the reaction rate doubles when the temperature is increased by 10 o C. 262

How do reactions get started? 263

How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. 264

How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. 265

How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. 266

How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. This relation explains the dependence of rate on concentration. 267

The preceding proportionality is oversimplified in one important respect. 268

The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. 269

The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy. 270

The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy. If the kinetic energies are large, then the molecules will vibrate so strongly that some chemical bonds will break – which is the first step towards the formation of products. 271

If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. 272

If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy E a. 273

If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy E a. Activation energy: The minimum energy with which molecules must collide to react. 274

275 NO + O 3 NO 2 + O 2

276 NO + O 3 NO 2 + O 2

We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. 277

We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules. 278

We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules. Normally, only a small fraction of these molecules – the very fast moving ones – can take part in a reaction. 279

280 The speeds of the molecules follow the Maxwell-Boltzmann distribution. Maxwell-Boltzmann distribution.

Energy level diagram for a chemical reaction. 281

Energy level diagram for a chemical reaction showing fraction of gas phase molecules that have the required energy to reach products. 282

Since a higher temperature gives rise to a greater number of energetic molecules – the rate of product formation is greater. 283

Arrhenius Equation 284

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as 285

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant 286

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy 287

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) 288

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) T is the temperature (Kelvin scale) 289

Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) T is the temperature (Kelvin scale) A is related to the collision frequency and is called the frequency factor (pre-exponent factor) 290

A second form of the Arrhenius equation, which is useful for the determination of E a, is obtained by taking the natural log of both sides of the Arrhenius equation. 291

Math Aside: Review of log properties. 292

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 293

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 294

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 295

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 296

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 297

Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 298

From the Arrhenius equation we have: 299

From the Arrhenius equation we have: 300